| 摘要: |
| 本文主要研究了带有一般梯度项的非线性抛物方程的矩阵型Li-Yau-Hamilton估计. 首先证明了当Riemann度量沿Ricci流演化时Riemann流形上非线性抛物方程的矩阵型Li-Yau-Hamilton 估计, 其次证明了当Kahler度量沿Kahler-Ricci流演化时Kahler流形上非线性抛物方程的矩阵型Li-Yau-Hamilton估计. |
| 关键词: 非线性抛物方程 Li-Yau-Hamilton估计 Ricci流 Kahler-Ricci 流 |
| DOI： |
| 分类号:O186.1 |
| 基金项目: |
|
| Matrix Li-Yau-Hamilton estimates for nonlinear parabolic equations |
|
Cao De Xia, Ren Xin An
|
| Abstract: |
| In this paper we are concerned with the matrix Li-Yau-Hamilton estimates for nonlinear
parabolic equations. Firstly, we derive such an estimate for nonlinear
parabolic equations on Riemannian manifolds with metric evolving under the Ricci flow. Then we consider the estimate for nonlinear
parabolic equations on Kahler manifolds with Kahler metrics evolving under the Kahler-Ricci flow. |
| Key words: nonlinear parabolic equation Li-Yau-Hamilton estimate Ricci flow Kahler-Ricci flow |
